Context. Gaia Data Release 2 (Gaia DR2) contains results for 1693 million sources in the magnitude range 3 to 21 based on observations collected by the European Space Agency Gaia satellite during the first 22 months of its operational phase. Aims. We describe the input data, models, and processing used for the astrometric content of Gaia DR2, and the validation of these results performed within the astrometry task. Methods. Some 320 billion centroid positions from the pre-processed astrometric CCD observations were used to estimate the five astrometric parameters (positions, parallaxes, and proper motions) for 1332 million sources, and approximate positions at the reference epoch J2015.5 for an additional 361 million mostly faint sources. These data were calculated in two steps. First, the satellite attitude and the astrometric calibration parameters of the CCDs were obtained in an astrometric global iterative solution for 16 million selected sources, using about 1% of the input data. This primary solution was tied to the extragalactic International Celestial Reference System (ICRS) by means of quasars. The resulting attitude and calibration were then used to calculate the astrometric parameters of all the sources. Special validation solutions were used to characterise the random and systematic errors in parallax and proper motion. Results. For the sources with five-parameter astrometric solutions, the median uncertainty in parallax and position at the reference epoch J2015.5 is about 0.04 mas for bright (G < 14 mag) sources, 0.1 mas at G = 17 mag, and 0.7 mas at G = 20 mag. In the proper motion components the corresponding uncertainties are 0.05, 0.2, and 1.2 mas yr −1 , respectively. The optical reference frame defined by Gaia DR2 is aligned with ICRS and is non-rotating with respect to the quasars to within 0.15 mas yr −1 . From the quasars and validation solutions we estimate that systematics in the parallaxes depending on position, magnitude, and colour are generally below 0.1 mas, but the parallaxes are on the whole too small by about 0.03 mas. Significant spatial correlations of up to 0.04 mas in parallax and 0.07 mas yr −1 in proper motion are seen on small (< 1 deg) and intermediate (20 deg) angular scales. Important statistics and information for the users of the Gaia DR2 astrometry are given in the appendices.

Context. The first data release from the Gaia mission contains accurate positions and magnitudes for more than a billion sources, and proper motions and parallaxes for the majority of the 2.5 million Hipparcos and Tycho-2 stars. Aims. We describe three essential elements of the initial data treatment leading to this catalogue: the image analysis, the construction of a source list, and the near real-time monitoring of the payload health. We also discuss some weak points that set limitations for the attainable precision at the present stage of the mission. Methods. Image parameters for point sources are derived from one-dimensional scans, using a maximum likelihood method, under the assumption of a line spread function constant in time, and a complete modelling of bias and background. These conditions are, however, not completely fulfilled. The Gaia source list is built starting from a large ground-based catalogue, but even so a significant number of new entries have been added, and a large number have been removed. The autonomous onboard star image detection will pick up many spurious images, especially around bright sources, and such unwanted detections must be identified. Another key step of the source list creation consists in arranging the more than 10 10 individual detections in spatially isolated groups that can be analysed individually. Results. Complete software systems have been built for the Gaia initial data treatment, that manage approximately 50 million focal plane transits daily, giving transit times and fluxes for 500 million individual CCD images to the astrometric and photometric processing chains. The software also carries out a successful and detailed daily monitoring of Gaia health.

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Bonded composite patches are very appropriate for aircraft structural repair, showing very good properties when compared with traditional mechanical fastening of metal sheets. The curing process of the composite patch must be done "onsite" and a direct resistive heating method has been proposed. The heat produced by the electric current through the Joule effect when crossing the patch carbon fibre bundles has been modelled with a Finite Element Program code, developed for the electric current equation. The heat conduction equation has also been modelled in the program, as well as the kinetics of the curing reaction of the composite resin. The electric resistivity of the materials is function of the temperature, so a nonlinear coupled system has been developed. Therefore, a complete simulation tool able to study different configurations, current intensities, materials, etc. for the composite patches is presented. A study case has been run with the developed code and results have been compared with experimental values. Good agreement is found.